In an Evolved Universal Mobile Telecommunications System Terrestrial Radio Access Network (E-UTRAN), an evolved node B (eNB) may be responsible for allocating wireless channel resources to accommodate device-to-device (D2D) discovery signal transmissions on the part of D2D-capable user equipment (D2D UEs) that wish to perform such transmissions. A given D2D discovery resource allocation may apply to a series of D2D discovery periods. Depending on an applicable discovery mode, an eNB may allocate D2D discovery resources in a UE-specific manner or a non-UE-specific manner. With respect to UE-specific D2D discovery resource allocation, in order to reduce the impact of the half-duplex constraint and/or randomize interference associated with in-band emissions, a resource hopping scheme may be utilized. According to such a resource hopping scheme, the particular subframes and/or subcarriers that are allocated to a UE for D2D discovery transmissions may vary across—and potentially within—D2D discovery periods.